I did something way different than a bucket of water and sandpaper....
I built my own contraption like this and as I was sanding with my right hand, I was holding the poly tubing above the sandpaper with my left hand... kept the sandpaper a lot cleaner and it had plenty of bite.

used 3M rubbing compound and 3M finesse-it polish with a variable speed buffer. Before and after photos. It takes time, patience and your arms will be sore but so worth it in the end.

my oxidation was worse, the shadowing contrast about the same, and I think my results came out a little better.... plus, I was able to wetsand out a couple of dings....
but, digital pics and computer screen don't look life real life.
I'm very happy with mine, as I'm sure you are also